Falling for Quantum Gravity

We’ve gone through Chapters 1, 2, 3 and 4 of Reality Is Not What It Seems. The abstract groundwork has been laid, the rhetorical lumber all trucked in, and now it’s time to start building a brand-spanking-new theory of reality!

Groovy. This particular post is my attempt to distill what I learned in Chapters 5, 6 and 7 of Rovelli’s treatise on quantum gravity.

Teeny Weenie Itsy Bitsy (and then Some)

As physicists started trying to make general relativity and quantum mechanics compatible with one another, they came up with a variety of ideas. One of them–the one Ravelli favors–is the idea of quantum gravity, an idea that hypothesizes that space itself can be be broken down into teeny, tiny basic components.

How tiny? Rovelli says they would Planck length, which he describes as follows:

The give an idea of the smallness of the scale we are discussing: if we enlarged a walnut shell until it had become as big as the whole observable universe, we would still not see the Planck length.

So, “tiny” doesn’t even begin to cover it. This is almost the definition of infinitesimal, assuming it actually exists outside the confines of the minds of the quantum gravity theorists.

Space Is a Reticulum

Sometimes quantum gravity is called “loop quantum gravity” because some solutions to what’s known as the Wheeler-DeWitt equation–which is seminal to this school of thought–depends on closed lines in space, aka loops.

Remember Faraday lines from “May the Forces Be With You”? Well, the loops are Faraday lines of the gravitational field (as opposed the electronic fields that Faraday was discovering). These lines are not just in space, according to the theory, they are the stuff from which space itself is woven. How cool is that? I makes me think of the Great Norns of Norse mythology, spinning time and space and the fate of humankind.

In a sense, then, space is an enormous reticulum (or “graph”) in which the lines intersect. The intersections are “nodes” and the lines themselves are “links.” Those nodes are the quanta of space. This means, according to the loop theory, that space is not a continuum, as has long been assumed. It’s made up of those fantastically small atoms of space (though space itself is the gravitational field, according to this theory).

More Networks, This Time Spinning

So, if the gravitational field is woven of these quantum particles of space, then how do we talk about specific networks of them? Well, the lines between the nodes are viewed as half-integers, and those integers are called “spin” in the lingo of quantum physics. And so….Rovelli calls these little networks “spin networks.” The networks “represent a quantum state of the gravitational field.”

I don’t know how to properly conceive spin networks, so for now I’m thinking of them as molecules. That is, atoms make up molecules and nodes make up spin networks. But this isn’t how Rovelli describes them so I’m probably way off.

One of the ways in which my molecule metaphor fails is that molecules actually exist as a thing (I think) whereas spin networks aren’t really entities at all. Rather, they are, like quantum particles, clouds of probabilities “over the whole range of all possible spin network.”

But they look pretty simple when depicted on the page:

Source: https://en.wikipedia.org/wiki/File:Spin_network.svg

The image above is identified as a spin network but, unlike the version in Rovelli’s book, the lines are not represented by half integers, which I thought represented the quantum spin. Still, you get the idea.

Let’s allow Rovelli sum it up for us:

At extremely small scale, space is a fluctuating swarm of quanta of gravity that act upon one another, and together act upon things, manifesting themselves in these interactions as spin networks interrelated with one another.

This leaves me visualizing thick clouds of mosquitos down in the Everglades, which may not be quite what he intended. But, ready or not, it’s time to deal with time.

Got No Time

According to Rovelli’s ideas, time doesn’t exist apart from the gravitational field. (Side note: Do we really need to keep calling it the gravitational field? Seems kind of lame for something this essential. How about The Lattice of Existence? Maybe The Network of God, or even The One True Reticulum? As I said before, physicists are usually shit as namers and even shittier as marketers, though I’d admit that stealing “quarks” from James Joyce was kind of genius.)

Anyhow, time pops out of this Lattice of Existence (trademark!).

This may seem a bit nuts, but Einstein has already taught us that time is elastic, relative and linked to velocity and gravity. So Rovelli is just doing Weird Al one better. In a sense, time ceases to exist altogether or at least it does at the Planck scale. Time is only the measure of how the loops and nodes interact. It is emergent.

Spinfoaming at the Mouth

We already discussed spin networks. Now let’s graduate to spinfoam, which sounds a lot like the suds one sees in one’s washing machine as it gyrates noisily away. Here’s how Wikipedia defines it: a topological structure that “consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman’s path integral description of quantum gravity.”

Does that help you? No, me either.

Let’s start again. The “foam” metaphor comes from the foam that you and I are familiar with. I think the image below is a very cool portrayal of literal foam, maybe helping us better visualize the network-like quality of spinfoam.


Paul VanDerWerf
 from Brunswick, Maine, USA: https://commons.wikimedia.org/wiki/File:Soap_Bubbles_(41493399275).jpg

And the “spin” part, of course, comes from the quantum mechanical notion of spin, to which we alluded earlier.

Rovelli writes that spinfoam “is made of surfaces that meet on lines, which in turn meet on vertices, resembling foam soap bubbles.” My impression is that spinfoam is a tool that merges two calculation techniques used by quantum physicists: a Feynman diagram and a lattice approximation. Rovelli provides more information about these but I’d clearly need a lot more education to understand them to my satisfaction.

You can see a representation of spinfoam here. Spinfoam is apparently what happens when a spin network moves through time. The lines become planes and the nodes become lines. You know how you can draw a series of stick figures on a small pad of paper and then flip the pages real fast to produce the illusion of moving animation? Well, that’s kind of what spinfoam is: the animation of the spin network moving forwards (or backwards!) in time.

The Universe Dresses Up in Spacetime but Is Secretly …

Rovelli argues that if you sand the universe down to the very bottom layer, you don’t find a beautiful hardwood floor (or spacetime or even oodles of particles). You find — dun dun dun! covariant quantum fields.

Hah, I bet you’re so surprised, thinking I was going to say “gravitational field”! But, no, now we have a new and equally wonky term that stumbles trippingly off the tongue: covariant quantum fields.

Sigh. More Star Trek jargon to be rattled off by Geordi La Forge on the bridge of the Enterprise.

As I said, physicists are shit at naming stuff.

On the other hand, they sure can weave a tale.

Nice job, Professor.

Featured Image: John Tenniel's illustration from The Nursery "Alice" (1889). See https://commons. wikimedia.org /wiki/File: Alice_drink_me.jpg

Einstein and the Big Squid

Taking the Red Pill of Relativity

Now things get weird. In the first post about Rovelli’s Reality Is Not What It Seems, we focused on atoms. Despite the strange fact that medieval Christians tried to censor the concept of atoms, they do not score very high on my weird-shit-o-meter. I was brought up with them, so they seem as friendly as eating potato chips on a comfortable couch.

In the second post, we got into electromagnetism. But, considering that most of us live enmeshed in cocoons of wire and wifi, it’s hard to see that topic as outlandish, however much our forebears would have been astonished.

But in Rovelli’s third chapter, the topic of this post, we’re forced to choke down a red pill if we want to enter the spacetime reality of Albert Einstein’s mind, thereby exiting The Matrix of our comfortable everyday reality where time and velocity seem as easy to grasp as a digital readout.

You’d think that by now we’d be accustomed to the original Weird Al’s big brain. I mean, we’ve had a century or so to get acclimated to this stuff. But, speaking for myself, I’m still struggling to cope with the idea that the world is not what it seems.

Present But Not Accounted For

Rovelli tries. But, despite the cartoons, his section on the “extended present” is hard to swallow. How and why has the present moment been extended by the Special Theory of Relativity?

I assume it has to do with the speed of light and relative time, but you’ll need to take it on faith within the context of this chapter. Here’s an example:

[O]n the moon, the duration of the extended present is a few seconds, and on Mars a quarter of an hour. This means we can say that on Mars there are events that are yet to happen, but also a quarter-of-an-hour of events during which things occur that are neither in our past nor in our future.

I find this hard to wrap my brain around and wish Rovelli had gone to greater lengths of explain the details. I remember getting a deeper glimpse of time relativity when pondering the ideas in the book Why Does E=mc2 (And Why Should We Care?), but I’ve since lost it (the glimpse, not the book). And now I’m wondering if I’ll need to bear down on that text again in order to grasp Rovelli’s arguments. We’ll see.

Space Is a Monster Mollusk

Okay, let’s put the “extended present” into a box (perhaps along with Schrodinger’s cat) and come back later to see what happened. For now, I want to focus on another statement in Chapter Three:

What if Newton’s space was nothing more than the gravitational field? This extremely simple, beautiful, brilliant idea is the theory of general relativity…. Newton’s space is the gravitational field. Or vice versa, which amounts to saying the same thing: the gravitational field is space….We are not contained within an invisible, rigid scaffolding: we are immersed in a gigantic, flexible mollusk (the metaphor is Einstein’s).

Okay, despite the Cthulhu vibe, I understand this better than the concept of extended present. I get the whole spacetime-curved-by-big-hunks-of-matter idea. I get that everything’s moving and has speeds only relative to everything else and everything is in constant flux. I even kind of (though not really) get the idea that time flows faster at the top of a mountain rather than in a valley.

But spacetime is the same thing as the gravitational field? Was that originally part of the Theory of Relativity? Apparently I’m not the only one confused. I wonder if that’s part of scientific history or just a tenet of the quantum gravity hypothesis, which is the ultimate subject of the book.

A Universe Designed by Escher

The latter sections of Chapter Three are mostly focused on how the universe may be a humongous globe with an extra dimension stuck in there. Einstein conceived a way in which the universe might be finite while still having no discernable boundary. Rovelli uses the metaphor of a globe:

On the surface of the Earth, if I were to keep walking in a straight line, I would not advance ad infinitum: I would eventually get back to the point from which I started. Our universe could be made in the same way. I fly around the universe and eventually end up back on Earth. A three-dimensional space of this kind, finite but without boundary, is called a “3-sphere.”

Although he goes on for another 12 pages or so, for me the above is the essence of the discussion. And, I kind of get it, or at least think I do, because we all understand the metaphor of the globe. Whether I can can truly conceive the shape of the universe like this, however, is another matter. It’s something to work on.

It’s Networks All the Way Down

Boiling it all down, I take away two main insights from this chapter. First is the idea that space as we (or at least I) sometimes think of it doesn’t exist. There are no vast empty spaces in space. It is jam-packed with gravitational and electromagnetic fields light waves, radio waves, gamma rays, microwaves, etc. In fact, maybe space is nothing more nor less than an unthinkably immense gravitational field.

Whatever space is, however, it’s certainly not mostly empty. It is a packed and fluctuating landscape in its own right. Jupiter is a not a planet but a mountain, one that we can climb and look down at the curved and rippling real estate of our solar system, if we’re willing to see beyond the merely visible.

My second insight is that network describes the scene even better than landscape. In my mind’s eye, I see block-and-tackle pulleys everywhere, connecting everything in our solar system (and the greater universe, of course) in a constantly shifting network.

Some mythologies have it that the Earth is supported on the back of a giant World Turtle. But what does the turtle stand on? There’s the old joke that, well, it’s “turtles all the way down” in a kind of infinite regress.

Perhaps it’s less of a joke to say that the universe is a network of networks. What do the networks attach to? Well, other networks via gravitational forces. I guess we could say it’s networks all the way down.

Featured image: Artist's concept of the Interplanetary Transport Network. The green ribbon represents one possible path from among the infinite number possible within the larger bounding tube. Constricted areas represent locations of Lagrange points. Wikimedia Commons